The shares of CornFlakes are trading at $105. Assume the yearly volatility of CornFlakes is equal to 20% at date 0, and changes after 3 months that for the next 3 months it is equal to 18% if the stock price has previously increased, and equal to 35% of the stock has previously decreased. The annualized risk-free rate is equal to 3%. Using a two-step binomial tree and the risk-neutral approach, obtain the prices of the following options with 6 months to maturity and strike price equal to $100:

European call option.

European put option.

Now assume a dividend of $8 is paid by CornFlakes in 3 months, obtain the prices of the following options with 6 months to maturity and strike price equal to $100:

American put option.

American call option.